A finite element for beams having segmented active constrained layers with frequency-dependent viscoelastics

Abstract

A finite element for planar beams with active constrained layer (ACL) damping treatments is presented. Features of this non-shear locking element include a time-domain viscoelastic material model, and the ability to readily accommodate segmented (i.e. non-continuous) constraining layers. These features are potentially important in active control applications: the frequency-dependent stiffness and damping of the viscoelastic material directly affects system modal frequencies and damping; the high local damping of the viscoelastic layer can result in complex vibration modes and differences in the relative phase of vibration between points; and segmentation, an effective means of increasing passive damping in long-wavelength vibration modes, affords multiple control inputs and improved performance in an active constrained layer application. The anelastic displacement fields (ADF) method is used to implement the viscoelastic material model, enabling the straightforward development of time-domain finite elements. The performance of the finite element is verified through several sample modal analyses, including proportional-derivative control based on discrete strain sensing. Because of phasing associated with mode shapes, control using a single continuous ACL can be destabilizing. A segmented ACL is more robust than the continuous treatment, in that the damping of modes at least up to the number of independent patches is increased by control action.

Piezoelectric Active Vibration Control of Damped Sandwich Beams

“…Recently, some methods, such as fractional derivatives, anelastic displacements "elds (ADF), Golla}Hughes}McTavish (GHM) and Yiu's, were proposed to model the frequency dependence of sti!ness and damping properties of viscoelastically damped structures [2]. Comparison between GHM, ADF and iterative modal strain energy (MSE) models has shown that both GHM and ADF, though increasing the system dimension, are superior to MSE for time-domain analyses of highly damped structures [3].…”

Vibroacoustical Analysis of Multiple-Layered Structures with Viscoelastic Damping Cores

“…The numerical stability and accuracy as well as for convergence issue of these four different FEM models were demonstrated by comparing the numerical results with those from experiments. Lesieutre and Lee [15] proposed a 3-node, 10 DOF FEM model for the threelayer ACL damping beam. This FEM model is advantageous in active control application due to its features of nonshear locking and adaptability to segmented constraining layers.…”

“…In the subsequent research, using a series of augment fields, the ATF model is able to model the damping material of higher loss factor with the weak frequency dependence. Remedying the limitation of 1D application, Lesieutre and Lee [15] proposed an anelastic displacement field (ADF) technique in 1996 and successfully extended its application from the 1-D problem to the 3-layer sandwich beam and 3-D problems.…”

“…Substituting the Biot damping model into (15), the dynamic equation with terms of the Biot parameters for ISRN Mechanical Engineering 5 the first viscoelastic material and terms for the second viscoelastic material can be developed as follows:…”

Optimization of viscoelastic systems combining robust condensation and metamodeling

“…Also, viscoelastic damping systems (specially, surface treatments) are prone to induce considerable mass additions. This last feature leads to the necessity of performing optimization aiming at achieving the desired performance and, at the same time, complying with design and construction constraints.In the last decades, much effort has been devoted to the development of finite element (FE) models capable of accounting for the typical dependence of the viscoelastic behavior with respect to frequency and temperature (Bagley and Torvik, 1983;MacTavish and Hughes, 1993;Lesieutre and Lee, 1996;Galucio et al, 2004). As a result, it is currently possible to model complex real-world engineering structures such as automobiles, airplanes, communication satellites, buildings and space structures (Balmès and Germès, 2002).…”